Nonlinear waves in a floating thin elastic plate, predicted by a coupled SPH and FEM simulation and by an analytical solution

This paper highlights linear and nonlinear waves under the influence of surficial structural stiffness and inertia. The main focus is on the waves in a thin elastic plate floating on the water surface. A numerical simulation method, combining smoothed-particle hydrodynamics and the finite element method, is developed to predict the waves propagating in the thin elastic plate. For validation, the simulation results are compared to those obtained through a numerical method, based on the linear potential theory for linear regular wave cases. When the incident wave amplitude was increased, the waves' nonlinearity was observed in the simulation results. The nonlinear waves' characteristics are elucidated through a mathematical solution derived in a similar manner to Stokes wave theory. A significant difference is confirmed through comparisons with the conventional, nonlinear, free-surface wave. The positive peak was higher than the negative peak due to nonlinearity in one frequency range, while it was the opposite in the other frequency range. The nonlinear wave's amplitude increased divergently at the frequency between the two frequency ranges. Overall, it is shown that the mathematical solution effectively explains the characteristics of the nonlinear waves in the elastic plate observed in the numerical simulations.